Finite Group Databasebeta

← C3×#73385 #11801922

Subgroups — C3×#73385 #11801922

Order 1152.

1137 conjugacy classes of subgroups.

The subgroup lattice has 331 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#872C211yesmaximal, characteristic
2C32×#376C211yesmaximal, characteristic, complemented
3C3×C4×(C2×D3)⋊C4C212yesmaximal
4C3×C4×Dic3⋊C4C212yesmaximal, complemented
5C3×C42×Dic3C211yesmaximal, characteristic, complemented
6C3×#4669C214yesmaximal
7C3×#4652C214yesmaximal, complemented
8C3×#2298—31nomaximal
9#73385C311yesmaximal, characteristic, direct product factor
10C22×C3×C4×D3C2211yescharacteristic
11C2×C32×C42C2212yes—
12C2×C32×C42C2211yescharacteristic
13C2×C3×(C2×D3)⋊C4C2214yes—
14C2×C3×(C2×D3)⋊C4C2212yes—
15C2×C3×Dic3⋊C4C2214yes—
16C2×C3×Dic3⋊C4C2212yes—
17C2×C3×C4×Dic3C2214yes—
18C2×C3×C4×Dic3C2212yes—
19C2×C3×C4×Dic3C2211yescharacteristic
20C3×#872C418yescomplemented
21C32×#95C2214yes—
22C3×C3⋊#95C2214yes—
23C3×C3⋊#95C2214yes—
24C2×C3×#117—31no—
25C2×#872C2×C311yescharacteristic
26C3×#388—34no—
27C3×#387—34no—
28C3×C4×C4⋊C4—32no—
29C3×C4×C22⋊C4—32no—
30C3×#376—21no—
31C3×#376D311yescharacteristic, complemented
32C3×#376C2×C311yescharacteristic, complemented
33C3×C43—31no—
34C4×(C2×D3)⋊C4C2×C312yes—
35C4×Dic3⋊C4C2×C312yescomplemented
36C42×Dic3C2×C311yescharacteristic, complemented
37#4669C2×C314yes—
38#4652C2×C314yescomplemented
39C23×C3×D3C2311yescharacteristic
40C22×C32×C4C2314yes—
41C22×C32×C4C2312yes—
42C22×C32×C4C2311yescharacteristic
43C22×C3×Dic3C2312yes—
44C22×C3×Dic3C2311yescharacteristic
45C22×C3×Dic3C2314yes—
46C2×C3×C4×D3—24no—
47C2×C3×C4×D3C2×C414yes—
48C32×C42—24no—
49C32×C42C2×C414yes—
50C3×(C2×D3)⋊C4—28no—
51C3×(C2×D3)⋊C4C2×C418yes—
52C3×Dic3⋊C4—28no—
53C3×Dic3⋊C4C2×C418yes—
54C3×C4×Dic3—24no—
55C3×C4×Dic3—28no—
56C3×C4×Dic3C2×C414yes—
57#2298—31noSylow
58C23×C3×C4—31no—
59C22×C4×D3C22×C311yescharacteristic
60C3×#117—38no—
61C2×C3×C4⋊C4—32no—
62C2×C3×C4⋊C4—34no—
63C2×C3×C22⋊C4—32no—
64C2×C3×C22⋊C4—34no—
65C2×C3×C42—22no—
66C2×C3×C42—21no—
67C2×C3×C42—31no—
68C2×C3×C42—34no—
69C2×C3×C42—32no—
70C2×C3×C42C2×D312yes—
71C2×C3×C42C2×D311yescharacteristic
72C2×C3×C42C22×C312yes—
73C2×C3×C42C22×C311yescharacteristic
74C2×(C2×D3)⋊C4C22×C314yes—
75C2×(C2×D3)⋊C4C22×C312yes—
76C2×Dic3⋊C4C22×C314yes—
77C2×Dic3⋊C4C22×C312yes—
78C2×C4×Dic3C22×C314yes—
79C2×C4×Dic3C22×C312yes—
80C2×C4×Dic3C22×C311yescharacteristic
81#872C3×C418yescomplemented
82C3×#95—24no—
83C3×#95—34no—
84C3×#95—34no—
85C3×#95C2×D314yes—
86C3×#95C22×C314yes—
87C3⋊#95C22×C314yes—
88C3⋊#95C22×C314yes—
89C23×C32C2411yescharacteristic
90C22×C3×D3—24no—
91C22×C3×D3—22no—
92C22×C3×D3C22×C412yes—
93C2×C32×C4—24no—
94C2×C32×C4—24no—
95C2×C32×C4—24no—
96C2×C32×C4—24no—
97C2×C32×C4C22×C414yes—
98C2×C32×C4C22×C412yes—
99C2×C32×C4#4114yes—
100C2×C3×Dic3—24no—
101C2×C3×Dic3—24no—
102C2×C3×Dic3—24no—
103C2×C3×Dic3—22no—
104C2×C3×Dic3C22×C414yes—
105C2×C3×Dic3C22×C412yes—
106C2×C3×Dic3#4118yes—
107C3×C4×D3—28no—
108C2×#117—31no—
109#388—34no—
110#387—34no—
111C4×C4⋊C4—32no—
112C4×C22⋊C4—32no—
113#376C3×D311yescharacteristic, complemented
114C43—31no—
115C24×C3—31no—
116C23×D3C23×C311yescharacteristic
117C22×C3×C4—21no—
118C22×C3×C4—24no—
119C22×C3×C4—22no—
120C22×C3×C4—31no—
121C22×C3×C4—34no—
122C22×C3×C4—32no—
123C22×C3×C4—34no—
124C22×C3×C4—64no—
125C22×C3×C4C22×D314yes—
126C22×C3×C4C22×D312yes—
127C22×C3×C4C22×D311yescharacteristic
128C22×C3×C4C23×C314yes—
129C22×C3×C4C23×C312yes—
130C22×C3×C4C23×C311yescharacteristic
131C22×Dic3C23×C311yescharacteristic
132C22×Dic3C23×C312yes—
133C22×Dic3C23×C314yes—
134C2×C4×D3—24no—
135C2×C4×D3C2×C3×C414yes—
136C3×C4⋊C4—38no—
137C3×C4⋊C4—68no—
138C3×C22⋊C4—38no—
139C3×C22⋊C4—68no—
140C3×C42—28no—
141C3×C42—24no—
142C3×C42—24no—
143C3×C42—24no—
144C3×C42—34no—
145C3×C42—68no—
146C3×C42—64no—
147C3×C42C4×D314yes—
148C3×C42C2×C3×C414yes—
149(C2×D3)⋊C4—28no—
150(C2×D3)⋊C4C2×C3×C418yes—
151Dic3⋊C4—28no—
152Dic3⋊C4C2×C3×C418yes—
153C4×Dic3—24no—
154C4×Dic3—28no—
155C4×Dic3C2×C3×C414yes—
156C22×C32C23×C411yescharacteristic
157C22×C32C2×#4112yes—
158C22×C32C2×#4114yes—
159C2×C3×D3—22no—
160C2×C3×D3—24no—
161C2×C3×D3—44no—
162C32×C4—24no—
163C32×C4—44no—
164C32×C4#11714yes—
165C3×Dic3—22no—
166C3×Dic3—24no—
167C3×Dic3—28no—
168C23×C4—31no—
169#117—38no—
170C2×C4⋊C4—32no—
171C2×C4⋊C4—34no—
172C2×C22⋊C4—32no—
173C2×C22⋊C4—34no—
174C2×C42—31no—
175C2×C42—32no—
176C2×C42—34no—
177C2×C42C2×C3×D312yes—
178C2×C42C2×C3×D311yescharacteristic
179#95—34no—
180#95—34no—
181#95C2×C3×D314yes—
182C23×C3—21no—
183C23×C3—32no—
184C23×C3—62no—
185C23×C3—64no—
186C23×C3C23×D311yescharacteristic
187C23×C3C24×C311yescharacteristic
188C22×D3—24no—
189C22×D3—22no—
190C22×D3C22×C3×C412yes—
191C2×C3×C4—24no—
192C2×C3×C4—24no—
193C2×C3×C4—28no—
194C2×C3×C4—24no—
195C2×C3×C4—24no—
196C2×C3×C4—24no—
197C2×C3×C4—24no—
198C2×C3×C4—24no—
199C2×C3×C4—24no—
200C2×C3×C4—22no—
201C2×C3×C4—24no—
202C2×C3×C4—24no—
203C2×C3×C4—34no—
204C2×C3×C4—32no—
205C2×C3×C4—38no—
206C2×C3×C4—44no—
207C2×C3×C4—44no—
208C2×C3×C4—44no—
209C2×C3×C4—64no—
210C2×C3×C4—62no—
211C2×C3×C4—64no—
212C2×C3×C4—64no—
213C2×C3×C4—68no—
214C2×C3×C4C2×C4×D314yes—
215C2×C3×C4C2×C4×D312yes—
216C2×C3×C4#23514yes—
217C2×C3×C4C22×C3×C414yes—
218C2×C3×C4C22×C3×C412yes—
219C2×C3×C4C3×#4114yes—
220C2×Dic3—24no—
221C2×Dic3—24no—
222C2×Dic3—24no—
223C2×Dic3—22no—
224C2×Dic3C22×C3×C414yes—
225C2×Dic3C22×C3×C412yes—
226C2×Dic3C3×#4118yes—
227C4×D3—28no—
228C2×C32C2×#11711yescharacteristic
229C2×C32C4×#4112yes—
230C2×C32#52914yes—
231C3×D3—42no—
232C24—31no—
233C22×C4—31no—
234C22×C4—34no—
235C22×C4—32no—
236C22×C4—34no—
237C22×C4—64no—
238C22×C4C22×C3×D314yes—
239C22×C4C22×C3×D312yes—
240C22×C4C22×C3×D311yescharacteristic
241C4⋊C4—38no—
242C4⋊C4—68no—
243C22⋊C4—38no—
244C22⋊C4—68no—
245C42—24no—
246C42—34no—
247C42—68no—
248C42—64no—
249C42C3×C4×D314yes—
250C22×C3—21no—
251C22×C3—22no—
252C22×C3—24no—
253C22×C3—62no—
254C22×C3—64no—
255C22×C3—124no—
256C22×C3C22×C4×D311yescharacteristic
257C22×C3C2×#23512yes—
258C22×C3D3×#4114yes—
259C22×C3C23×C3×C411yescharacteristic
260C22×C3C2×C3×#4112yes—
261C22×C3C2×C3×#4114yes—
262C2×D3—22no—
263C2×D3—24no—
264C2×D3—44no—
265C3×C4—24no—
266C3×C4—24no—
267C3×C4—24no—
268C3×C4—44no—
269C3×C4—48no—
270C3×C4—44no—
271C3×C4—44no—
272C3×C4—62no—
273C3×C4—64no—
274C3×C4—68no—
275C3×C4#87214yes—
276C3×C4C3×#11714yes—
277Dic3—22no—
278Dic3—24no—
279Dic3—28no—
280C32#229811yescharacteristic, complemented, Sylow
281C23—32no—
282C23—62no—
283C23—64no—
284C23C23×C3×D311yescharacteristic
285C2×C4—24no—
286C2×C4—24no—
287C2×C4—24no—
288C2×C4—24no—
289C2×C4—34no—
290C2×C4—32no—
291C2×C4—38no—
292C2×C4—64no—
293C2×C4—62no—
294C2×C4—64no—
295C2×C4—64no—
296C2×C4—68no—
297C2×C4C2×C3×C4×D314yes—
298C2×C4C2×C3×C4×D312yes—
299C2×C4C3×#23514yes—
300C2×C3—22no—
301C2×C3—24no—
302C2×C3—21no—
303C2×C3—122no—
304C2×C3C2×#87211yescharacteristic
305C2×C3#552212yes—
306C2×C3#552814yes—
307C2×C3C2×C3×#11711yescharacteristic
308C2×C3C3×C4×#4112yes—
309C2×C3C3×#52914yes—
310D3—42no—
311C22—64no—
312C22—62no—
313C22—124no—
314C22C22×C3×C4×D311yescharacteristic
315C22C2×C3×#23512yes—
316C22C3×D3×#4114yes—
317C4—24no—
318C4—44no—
319C4—64no—
320C4—68no—
321C4—62no—
322C4C3×#87214yes—
323C3—21no—
324C3#7338511yescharacteristic, direct product factor
325C3C3×#229811yescharacteristic, complemented
326C2—122no—
327C2C2×C3×#87211yescharacteristic
328C2C3×#552212yes—
329C2C3×#552814yes—
subgroupG/H
centerC22×C3×C4C22×D3
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
FittingC32×#376C2
socleC23×C32C24
prime radicalC23×C3×D3C23
cosocleC23×C3C24×C3
hypercenterC3×#376D3
hypocenterC3C3×#2298
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3×C4 ◁ C3×#376

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C32×#376C2semidirect
4. C3×C4×Dic3⋊C4C2semidirect
5. C3×C42×Dic3C2semidirect
7. C3×#4652C2semidirect
9. #73385C3direct (N × H)
20. C3×#872C4semidirect
31. C3×#376D3semidirect
32. C3×#376C2×C3semidirect
35. C4×Dic3⋊C4C2×C3semidirect
36. C42×Dic3C2×C3semidirect
38. #4652C2×C3semidirect
81. #872C3×C4semidirect
113. #376C3×D3semidirect
280. C32#2298semidirect
324. C3#73385direct (N × H)
325. C3C3×#2298semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C3×#8722
C32×#3762
C3×C4×(C2×D3)⋊C42
C3×C4×Dic3⋊C42
C3×C42×Dic32
C3×#46692
C3×#46522
C3×#22983
#733853